Technically would result in an overburdened network. Your phone will be trying to connect to the tower at maximum speed available, thus using up the same bandwidth you would be using up by actually using the network that powers the tower. There is no bandwidth problem of the network that powers the towers, the problem is the actual radio spectrum overcrowding...

Of course the phone will be able to connect to the network at max speed, it's the bandwidth that is limited and that is all software. As for techically being possible... well, it ALREADY IS in country-wide use here in Finland, all major operators do it and it works just peachy.